The Breslow approximation treats every tied event as facing the full
risk set, which over-counts it: with many ties the partial likelihood
is too flat and beta is attenuated toward zero. It is the cheap
option and the default in some software; morie_efron_tie_correction
costs almost nothing more and is closer to the exact discrete
likelihood.
Usage
morie_breslow_tie_correction(time, event, X, ...)
Arguments
- time
follow-up times, non-negative.
- event
1 for an event, 0 for right-censored.
- X
covariate matrix, one row per subject.
- ...
passed to the fitter (max_iter, tol,
offset).
Value
list with beta, se, z, p_value,
hazard_ratio, loglik, information, and the
data needed by the residual functions.
References
Breslow, N. (1974). Covariance analysis of censored
survival data. Biometrics, 30(1), 89-99.
Examples
set.seed(1)
X <- matrix(rnorm(120), ncol = 2)
tt <- rexp(60, exp(X %*% c(0.7, -0.4)))
morie_breslow_tie_correction(tt, rep(1, 60), X)$hazard_ratio
#> [1] 2.0413156 0.5802592
